Preheat the oven to 350 degrees. Grease a 9 x 13 inch pan with butter or shortening.
To make the crust, whisk together the flour, sugar, lemon zest, and salt in a bowl. Cut the butter into cubes then add them to the bowl. Use a pastry cutter to cut the butter into the flour, working the dry ingredients into the butter until the mixture is in small, sandy clumps. Pour the mixture into the greased pan, spreading it evenly to the edges. Use your fingers to pat it down until smooth and firm. Bake for 18-22 minutes or until golden brown on the edges. Remove from the oven.
Meanwhile, prepare the filling. In a stand mixer, beat the eggs on medium speed for about 2 minutes. Gradually add the sugar, and continue to beat until light and creamy. Add the flour and lemon juice. Beat on low speed until just combined.
When the crust is removed from the oven, spread the raspberries evenly over the top. Gently pour the filling over top of the raspberries and the warm crust. Bake for an additional 18-20 minutes or until the center is no longer jiggly.
Allow the bars to cool, refrigerate for 1-2 hours, then sprinkle with powdered sugar and serve. Bars can be stored covered in the fridge for up to 3 days, but are best enjoyed within 24 hours.